Time Series Denoising Using Nonlinear Schrödinger Equation

In order to remove noise in time series with quantities of noise,a denoising method based on dy-namical stochastic resonance is presented.By analyzing the dynamical stochastic resonance in nonlinear op-tical systems,the nonlinear disturbance in nonlinear Schrödinger equation is derived,the propagation model is obtained and applied to time series denoising.Firstly,the time series signal is normalized as system input.Then the parameters of the system propagation equation are determined by the adaptive particle swarm op-timization algorithm.The numerical solution of the propagation equation is obtained by the split step Fourier method as system output.Compared with the existing denoising methods,proposed method improves sig-nal-to-noise ratio by 0.3‒3.7 dB,reduces by 0.03‒0.11 on average for typical time series signals.Experi-mental results show the better denoising ability of proposed method.